In: Wagner W., Sz6kely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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I 
SELF CALIBRATION OF SMALL AND MEDIUM FORMAT DIGITAL CAMERAS 
Donald Moe a , Aparajithan Sampath 3 , Jon Christopherson 3 , Mike Benson b 
a SGT, Inc 1 , U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) Center, Sioux Falls, SD 
57198 USA-(dmoe, asampath, jonchris)@usgs.gov 
b U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) Center, Sioux Falls, SD 57198 
USA - benson@usgs.gov 
KEY WORDS: Photogrammetry, Rectification, Bundle, Camera, Geometric. 
ABSTRACT: 
The knowledge of a camera’s interior orientation parameters are a prerequisite for the camera to be used in any precision 
photogrammetric project. Historically, the interior orientation parameters have been determined by analyzing the measured ground 
3D coordinates of photo-identifiable targets, and their 2D (image) coordinates from multiple images of these targets. Camera self 
calibration, on the other hand, uses targets on a scene that have not been measured before. In this research, we will briefly discuss 
existing self calibration techniques, and present two methods for camera self calibration that are being used at the U.S. Geological 
Survey’s Earth Resources Observation and Science (EROS) Data Center. The first method, developed by Pictometry (augmented by 
Dr C.S. Fraser), uses a series of coded targets on a cage. The coded targets form different patterns that are imaged from nine different 
locations with differing camera orientations. A free network solution using collinearity equations is used to determine the calibration 
parameters. The coded targets are placed on the cage in three different planes, which allows for a robust calibration procedure. The 
USGS/EROS has developed an inexpensive method for calibration, particularly for calibrating short focal length cameras. In this 
case, the coded targets are pasted on a small prototype box and imaged from different locations and camera orientations. The design 
of the box is discussed, and the results of the box and the cage calibrations are compared and analyzed. 
1. INTRODUCTION 
1.1 General 
Camera calibration procedure aims to completely characterize 
the path of a ray of light that enters a camera, at the time of 
exposure. The parameters that are used for this characterization 
are termed the interior orientation parameters. The main 
parameters are the focal length of the lens and the location of 
the principal point of symmetry. However, for photogrammetric 
purposes, the knowledge of the deviation of the light ray from a 
straight line, described by polynomial coefficients, is also 
important. This deviation is termed lens distortion, and the 
polynomial coefficients are termed lens distortion parameters. 
The United States Geological Survey (USGS) has the 
responsibility for camera calibration in the United States (Lee, 
2004). In this research, we shall present two methods used by 
the USGS to determine these parameters for small and medium 
format digital cameras. The first method, developed by 
Pictometry(augmented by Dr C.S. Fraser), uses a series of 
coded targets on a cage. The coded targets are placed on the 
cage in three different planes, which allows for a robust 
calibration procedure. The second method describes the 
development of a method whereby the coded targets are pasted 
on a small prototype box. The importance of calibrating a 
camera used for photogrammetric purposes cannot be 
overstated. While it is possible to obtain accurate ortho 
products without a well calibrated camera, these would require 
a very dense network of control points. Such a network will 
make a photogrammetric project prohibitively expensive. 
Symbol 
Description 
f 
Gaussian focal length 
K 1} K 2> K 3 
Parameters for radial 
distortion 
Pl,p 2 
Parameters for decentering 
distortion 
B b B 2 
Differential scale distortion 
(for digital cameras) 
X P’ y P 
Position of the principal 
point of symmetry with 
respect to the array pixel 
frame. 
Table 1. List of interior orientation parameters 
1.2 Camera calibration methods 
There are many approaches to camera calibration. With the 
increasing popularity of the field of Computer Vision as an area 
of research, the methods have increased. Camera calibration 
methods preferred by photogrammetrists can be categorized 
broadly into three classes. 
'Work performed under U.S. Geological Survey contract 08HQCN0005